Pennsylvania Gov. Richard L. Thornburgh has a problem practically at his office doorstep that might discourage many a politician from even thinking of reelection. Three years of haggling and hundreds of millions of dollars of expenditures haven't been able to solve it.
Yet this problem - the crippled and world-famous nuclear power plant at Three Mile Island, a short distance downriver from this capital city - isn't even an issue in the governor's reelection bid.
Instead, Mr. Thornburgh's prospects at the polls almost certainly will rise or fall on the strength of Pennsylvania's now wobbly economy.
By all accounts, in the 31/2 years since he was elected, Thornburgh demonstrated calm leadership during the Three Mile Island crisis, has presided over the cleaning up of a previously scandal-ridden state government, kept taxes down, effected needed welfare reform, and trimmed thousands of surplus jobs from the state payroll. Even his critics concede that he has been an efficient administrator.
Moreover, he has an attractive running mate in Lt. Gov. William Scranton III, no opposition in the May 18 primary, and a Democratic rival for the general election in November whom many Pennsylvanians have never heard of.
Still, says a key aide, ''We're running scared.''
The reason: Thornburgh has chosen to align himself closely and visibly with the controversial economic policies of President Reagan - a decision he defends but which critics say is risky in view of Pennsylvania's 11 percent unemployment rate and the weakened condition of its basic industries - steel, coal mining, and heavy manufacturing.
The economy notwithstanding, none of the best-known Democrats in the state - notably Philadelphia Mayor William Green III, former auditor general Robert P. Casey, Pittsburgh Mayor Richard Caligiuri, and 1978 gubernatorial candidate Peter Flaherty - wanted to take on Thornburgh in 1982. So the task has fallen to three-time US Rep. Allen Ertel.
Mr. Ertel, from conservative, traditionally Republican central Pennsylvania, is a moderate who not only beat back all GOP opposition but outran President Reagan in his district in 1980. Like Thornburgh, he built a reputation for honesty and fairness as a public prosecutor.
He, too, lacks significant opposition in the primary. He has the endorsements of such influential organizations as the state AFL-CIO and the Pennsylvania State Education Association (PSEA), the state's largest teachers union.
But his party is in debt and struggling to reorganize after years of infighting, and he starts far behind Thornburgh in terms of name recognition and money for campaigning.
Ertel campaign manager John Plebani, however, thinks Thornburgh is vulnerable for not being responsive to problems that most concern Pennsylvanians.
''For some reason, our unemployment is higher here than that in New York, New Jersey, Maryland, or Delaware,'' he says. ''Those are all states in our area with the same kinds of basic industry and infrastructure that we have. Maybe it's because we haven't been as imaginative as we can be in attracting new industry, in using our various state resources, in targeting those things we do to create new industries.''
Retorts the governor: ''I have yet to hear any specific, positive suggestions from the opposition. . . . They act as if somehow Pennsylvania is an island of unemployment in an otherwise booming economy. It just isn't so. Our unemployment rate is the 11th highest in the nation, and it's too high, but there are limits to what we can do about it.''
Next to the state of the economy, the key issue here seems to be Thornburgh's split with the 130,000-member PSEA. The union backed candidate Thornburgh in 1978 over Mr. Flaherty, but now accuses him of reneging on a campaign promise to seek increased state aid to public education.
The PSEA has given Ertel $25,000 so far in campaign funds and intends to give more after the primary, says political director Walt Carmo. ''As hard as we say we want to work for Ertel, that's how hard we tried for Thornburgh last time,'' he says. ''We want a pro-education governor, a governor who will honor commitments.''
Thornburgh dismisses the PSEA challenge as ''a vicious personal and political vendetta against me'' and says ''we have not been stingy with education.''
PSEA, says former lieutenant governor Ernest Kline, now a Harrisburg political consultant, ''can be effective in the general election - to some extent.'' But, he adds, the union's tactics could have the unintended effect of generating support for Thornburgh among voters who foresee their taxes going up to pay for new aid to education.
The governor's political operatives, he says ''are smart; they don't get trapped into those kinds of things.''